arXiv subjects

Chunxi Jiao

Publications and source records attributed to Chunxi Jiao.

6 recordsLinked to original sources

arXiv2026

Local Exact Controllability of Landau-Lifshitz-Gilbert Equation

We prove a local exact controllability result for controlled Landau--Lifshitz--Gilbert equations on $\mathbb T^2$: if the initial energy is sufficiently small, then for any terminal time $T>0$, there is a localised external magnetic field such that the system can be steered exactly to the terminal value of any nearby uncontrolled trajectory. We first transform the equation to a quasilinear parabolic system on $\mathbb R^2$ by a suitable stereographic chart. Then the Carleman estimate is established for the linearised system through a decomposition adapted to the self-adjoint and skew-adjoint structure of the conjugated adjoint operator. This yields observability and $L^\infty$-null controllability for the linearised system. The nonlinear projected equation is then recovered by a Kakutani fixed-point argument. We also obtain a semi-global controllability result under a hemisphere condition.

math.AP↗

arXiv2025

Pathwise Solvability and Bubbling in 2D Stochastic Landau-Lifshitz-Gilbert Equations

We investigate the stochastic Landau-Lifshitz-Gilbert (LLG) equation on a periodic 2D domain, driven by infinite-dimensional Gaussian noise in a Sobolev class. We establish strong local well-posedness in the energy space and characterize blow-up at random times in terms of energy concentration at small scales (bubbling). By iteration, we construct pathwise global weak solutions, with energy evolving as a c{à}dl{à}g process, and prove uniqueness within this class. These results offer a stochastic counterpart to the deterministic concept of Struwe solutions. The approach relies on a transformation that leads to a magnetic Landau-Lifshitz-Gilbert equation with random gauge coefficients.

math.AP↗

arXiv2023

Lévy flights as an emergent phenomenon in a spatially extended system

Anomalous diffusion and Lévy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate signals. Mathematicians have recently unveiled mechanisms to generate anomalous diffusion, both stochastically and deterministically. However, there exists to the best of our knowledge no explicit example of a spatially extended system which exhibits anomalous diffusion without being explicitly driven by Lévy noise. We show here that the Landau-Lifshitz-Gilbert equation, a stochastic partial differential equation (SPDE), despite only driven by Gaussian white noise, exhibits superdiffusive behaviour. The anomalous diffusion is an entirely emergent behaviour and manifests itself in jumps in the location of its travelling front solution. Using a collective coordinate approach we reduce the SPDE to a set of stochastic differential equations (SDEs) driven by Gaussian white noise. This allows us to identify the mechanism giving rise to the anomalous diffusion as random widening events of the front interface.

math.DS↗

arXiv2023

Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents

We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated ferromagnet with competing first and second order exchange interactions exposed to deterministic and random spin transfer torques in form of transport noise. We prove the existence and pathwise uniqueness of weak martingale solutions in the energy space. The result ensures the persistence of topological patterns, occurring in such magnetic systems, under the influence of a fluctuating spin current.

math.PR↗

arXiv2022

Numerical method and Error estimate for stochastic Landau--Lifshitz--Bloch equation

We study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau-Lifshitz-Bloch (LLB) equation on a bounded domain in $\mathbb R^d$ for $d=1,2$. Our main results are estimates of the rate of convergence of the Finite Element Method to the solutions of stochastic LLB. To overcome the lack of regularity of the solution in the case $d=2$, we propose a Finite Element scheme for a regularised version of the equation. We then obtain error estimates of numerical solutions and for the solution of the regularised equation as well as the rate of convergence of this solution to the solution of the stochastic LLB equation. As a consequence, the convergence in probability of the approximate solutions to the solution of the stochastic LLB equation is derived. To the best of our knowledge this is the first result on error estimates for a system of stochastic quasilinear partial differential equations. A stronger result is obtained in the case $d=1$ due to a new regularity result for the LLB equation which allows us to avoid regularisation.

math.NA↗

arXiv2022

Existence, uniqueness and regularity of solutions to the stochastic Landau-Lifschitz-Slonczewski equation

In this paper we are concerned with the stochastic Landau-Lifshitz-Slonczewski equation (LLS) that describes magnetisation of an inifnite nanowire evolving under current driven spin torque. The current brings into the system a multiplicative gradient noise that appears as a transport term in the equation. We prove the existence, uniqueness and regularity of pathwise solutions to this equation.

math.AP↗